The purpose of this study is to show that H-2 is easily dissociated on lithium edge decorated carbon systems to form strong C-H and Li-H bonds. This mechanism has not been considered in previous studies where these kinds of systems have been proposed as good candidates to serve as hydrogen storage materials. The reactivity of molecular hydrogen H-2 on three representative lithium edge-decorated carbon systems on the clusters C6Li7+ 1 and C6Li6 2, and on lithium edge -decorated zig-zag graphene nanoribbon GNR-Li 3 have been studied using ab initio calculations based on the density functional theory with dispersion-corrected van der Waals exchange correlation functional. Our calculations show, on the one hand, that heterolytic hydrogen dissociation can precede with relatively low reaction barriers 0.60, 0.45 and 0.56 eV for systems 1, 2 and 3, respectively along the minimum energy path and, on the other hand, that chemisorption energies are highly stabilizing in the range of 1.15-1.54 eV. It is important to note that the highest activation barrier is found for the unique system, characterized as global minimum, on its corresponding potential energy surface PES, which is system 1. These findings suggest that reversibility of the hydrogen absorption-desorption reactions, required in promising hydrogen storage materials, does not apply in these systems.Nota general